complex downconversion of signal

[sunil]

Hi,
I have a doubt regarding 'complex' downconversion of a 'real' bandpass signal.Lets say the real bandpass(BP) signal having a bandwidth od BHz at centre frequency Fc has to be downconverted to a complex basedband signal. If we multiply the the signal by a an exponential signal say e^(-jFc),what will be the result.Can someone explain this pictorially(spectrum ) what happens to the positive and negative frequency components of the bandpass signal.
Thanks

[Ankit Modi]

If you have a BP(band pass) signal at 'Fc' with bandwidth 'B' hz then multplying it by exp(-j2*pi*Fc*t) will convert it into a LP signal. To view pictorially imagine ur BP signal as a rectangular box at freuency Fc and having amplitude say "A" (and it has a bandwidth "B".) same for negative frequencies(which will be on the negative axis, center "-Fc"). The downconversion operation will move both boxes(-ve and +ve frequencies) to zero frequency. The amplitue will double and become '2A' and the bandwidth will be halved--'B/2'.
This is because the up-conversion moved the LP signal spectrum to the center freuency Fc, this opertaion doubles the bandwidth of the signal and reduces the amplitude by half.
To clearly understand the concept do it mathematically also. There are several textbooks available which explain this in detail.
hope this helps.
Ankit